Space-Time Block Codes for Wireless Systems - The ...

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In this work, we present a general model for space-time DS-CDMA signals in a multipath fading channel, and focus on performance analysis and code design as a function of spreading code correlation and multipath fading. Both uplink and downlink scenarios are considered. Furthermore, the framework is general enough to encompass non-spread systems with slight modification (Section 2.4). Note that multipath fading is a consequence of signal bandwidth exceeding channel coherence bandwidth. Rich multipath fading is usually observed in spread systems where signal usually occupy large bandwidth which exceeds channel coherence bandwidth. Non-spread systems may also experience multipath fading [TNSC99], although less severe than spread systems. One consequence of multipath fading is that the optimal decoder is a block sequence decoder, however, with typical channel assumptions, we show that the code design based on the worst case pairwise error probability analysis remains a block optimization problem. The presence of multiple access and spreading make code design for spread systems different from that of non-spread systems. The differences in both the design criteria and the resultant optimal codes for spread and non-spread systems are highlighted. Due to the assumption of independent channels, at the uplink, the multiuser coding problem decouples to multiple single user coding problems; in contrast, the downlink space time coding problem is truly a multiuser problem. At the uplink, all the transmissions of different users are asynchronous, but this does not affect the performance analysis and code design due to the decoupling among users. Based on the design criteria, which is related to spreading code correlation, this work further attempts to optimize codes based on coding gain. The found codes, deemed Optimal Minimum Metric (OMM) code, provide solid gains over known codes which have more structure, like orthogonal codes [TJC99, Ala98] and unitary group codes [SHHS01], in flat/multipath fading channels and single-user/multiuser systems. The search for optimized codes is simplified through “isometries”, transformations to which the design metrics are invariant. For more detailed discussion on isometry, please refer to Section 4.2. We also analyze some methods to construct space-time codes and show their performance with respect to spreading code correlation. The structure of optimized codes leads to the construction of nonlinear hierarchical codes [GM03b]. The effect of the multipath fading channel on code performance is evaluated. As expected, with perfect CSI, multipath provides a higher diversity level. Spread systems can 7
easily achieve maximum diversity (the number of transmit antenna times the number of multipaths for one receive antenna), while non-spread systems must satisfy more stringent conditions to achieve full diversity. A similar, but weaker result was presented in [TNSC99], which showed that a space-time code will achieve at least the same diversity in a multipath fading channel as it does in a flat fading channel. Herein, the exact diversity level is easily determined. Based on the observation on diversity level, [TNSC99] concludes that a space-time code designed for a slow flat fading channel will continue to perform well in a multipath fading channel, we will further show that this conclusion also holds in terms of coding gain when the multipath delay spread is relatively small in comparison to the symbol interval duration. This chapter is organized as follows. Section 2.2 derives the performance criteria and code design principles in the uplink. Section 2.3 discusses the downlink. Section 2.4 briefly describes the non-spread system. Section 2.5 tabulates some of the optimized codes found via computer search, compares their performance with some known codes, and analyzes properties of these codes. Section 2.6 considers some application issues for the quasi-static channel: invariant operations, the sensitivity of code performance to spreading code correlation, and some suboptimal methods for constructing spacetime codes. Finally, conclusions and some suggestions for future work are discussed in Section 2.7. 2.2 The Uplink In this section, we provide a general space-time model for the uplink of DS-CDMA systems. The generality of the formulation incurs some added complexity, but offers the advantage of enabling analysis of coding gain as a function of the spreading code correlation. If the channel coefficients of different receive antennae are uncorrelated and the Maximum-Likelihood decoder is employed, multiple receive antennae will not affect code design based on worst case PEP analysis (but do affect performance). Recent work shows that as the number of receive antennae increases, the multi-input multi-output fading channel model approaches a multiple parallel AWGN channel model; as such different design metrics should be considered for the large number of receive antennae case [GF01, CYV99]. Herein, we consider a small to moderate number of receive antennae, 8
Page 1 and 2: COMMUNICATION SCIENCES INSTITUTE
Page 3 and 4: Dedication This dissertation is ded
Page 5 and 6: Contents Dedication Acknowledgement
Page 7 and 8: List Of Tables 2.1 The distance spe
Page 9 and 10: 3.4 The BLUE and LS estimators have
Page 11 and 12: Abstract Space-time codes are effec
Page 13 and 14: spreading. The focus of [HMP01] is
Page 15 and 16: 5, respectively: first, for an arbi
Page 17: Chapter 2 Space-Time Block Codes in
Page 21 and 22: For example, a BPSK 2 × 2 block co
Page 23 and 24: multipaths corresponding to each tr
Page 25 and 26: where G(t) = [G (1) (t), . . . . .
Page 27 and 28: where D α and D β are two codewor
Page 29 and 30: For the quasi-static fading channel
Page 31 and 32: and the non-zero segment of any lin
Page 33 and 34: Let us consider the issue of achiev
Page 35 and 36: as A and B respectively, and observ
Page 37 and 38: L c = 1 0 7 9 14 0 0.00 30.56 16.00
Page 39 and 40: where D (k) (t) is defined in Equat
Page 41 and 42: For this special case of fixed spre
Page 43 and 44: where ˜R = ŘT 1 Ř−1 2 Ř 1 . (
Page 45 and 46: 2.5 Optimal Minimum Metric Codes In
Page 47 and 48: index ρ c rate size constl OMM 1 1
Page 49 and 50: 16 0 9 32-16ρ 2 32-16ρ 2 16 16 16
Page 51 and 52: Class ρ ∆ p (ζ v ) N p code ind
Page 53 and 54: 2. In a spread system (ρ = 0.3), t
Page 55 and 56: 10 0 SNR OMM spread orthogonal 10
Page 57 and 58: ρ c =0.3 10 0 SNR Rate 1 4X2 2 Rat
Page 59 and 60: Code Comparison, Joint ML Decoder,
Page 61 and 62: 2.6 Practical Considerations In thi
Page 63 and 64: 2.6.2 Sensitivity to Correlation Us
Page 65 and 66: structure ] 1 structure ] 2 structu
Page 67 and 68: Chapter 3 On Suboptimal Linear Deco
Page 69 and 70:
where σ t is signal-to-noise ratio
Page 71 and 72:
decorrelator. Denote ‖x‖ 2 R x
Page 73 and 74:
3.4 The Mapper Recall that the outp
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Now we evaluate the overall decoder
Page 77 and 78:
and lim L HH R 3 H = r→∞ L r [1
Page 79 and 80:
the FIM for random d is [ ∂ ln P
Page 81 and 82:
Apparently R d is singular, which i
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L t =2, L r =1, K=1, ρ=0.3, ignori
Page 85 and 86:
L t =2, L r =2, K=1, ρ=0.3, two re
Page 87 and 88:
Chapter 4 Nonlinear Hierarchical Co
Page 89 and 90:
signal corresponding to N c symbol
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1. full diversity ∆ H (D i − D
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epresent both for convenience. All
Page 95 and 96:
We may construct the whole set from
Page 97 and 98:
2. Most right isometries P are redu
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★ ✥ S k ✧ a U j , P j ✲ b
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3. Given Isometries U k U j and P j
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[ 2 ] [ 168 ] [ 42 ] [ 128 ] 1 1
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which are very likely to be optimal
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4X3 BPSK(8 Codewords) and QPSK(64 C
Page 109 and 110:
Chapter 5 Regular Multiple Trellis
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The high rate performance is poor,
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ehavior of a regular trellis are: t
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All the NHCs found in this work sat
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Whenever there exist parallel trans
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M m g=1 g=2 g=4 g=8 next jump b=2 2
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provides a lower bound on the numbe
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Label S k S Comment Figure 1/2 I2S2
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Label S k O(= gbp) S(= gb) Figure 1
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2X2 QPSK, |S 5 |=32 codewords 10 0
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S k d S k S k ′ d H S 1 (1, 1, 1,
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Rate 6/2 2X2 8PSK, |S 7 |=128 vs |S
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1 172 251 330 1 1 1 304 413 486 87
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Rate 5/3, 3X3 QPSK, |S 7 |=128 Code
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parameters: the number of trellis g
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[DS87] D. Divsalar and M. K. Simon.
Page 141 and 142:
[SHHS01] [Sle68] A. Shokrollahi, B.
Page 143 and 144:
ù"ú"ú"û ù"ü"ù ù"ý0øJþ ÿ
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©¤¥¢©©©©¤©¤©©¤©¤©
Page 147 and 148:
J;KL4MNL=L;L0K=O;P=Q;ORO=Q;O=Q;Q;MN
Page 149 and 150:
0 1 14 1 7 8 Figure B.2: 2 × 2 BPS
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0 2 168 42 128 93 247 117 223 1 30
Page 153 and 154:
0 2 168 42 128 93 247 117 223 30 18
Page 155:
0 2 168 42 128 93 247 117 223 30 18
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